This paper proposes a class of dual-band bandpass filters with λ/4 stepped-impedance resonators (SIRs) and presents a rigorous synthesis method for these compact filters. Firstly, λ/4 SIRs are designed to generate their first two resonant modes in the two specified passbands, and they are sequentially cascaded by alternative J and K inverters. In design, λ/4 SIRs need to be chosen not only to satisfy the prescribed dual-band central frequencies, but also to compensate for the deficient values of K inverters at these two frequencies. Following that, a generalized synthesis method is extensively described for design and exploration of novel dual-band filters on the microstrip-line topology. The two types of second-order dual-band Chebyshev bandpass filters with dual passbands are at 5.8 and 1.8 GHz (large frequency ratio), as well as 5.8 and 2.4 GHz (small frequency ratio), respectively. Furthermore, a fourth-order dual-band filter is designed using the proposed synthesis method to demonstrate improved dual-passband performance with sharpened out-of-band rejection skirts and high in-between-band isolation. Finally, five filter prototypes are fabricated for the experiment, and both simulated and measured results validate the theoretical ones successfully.